About the Book

Explaining how to apply to mathematical programming to network design and control, Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to more advanced concepts, its comprehensive coverage provides readers with a solid foundation in mathematical programming for communication networks.

Addressing optimization problems for communication networks, including the shortest path problem, max flow problem, and minimum-cost flow problem, the book covers the fundamentals of linear programming and integer linear programming required to address a wide range of problems. It also:

Examines several problems on finding disjoint paths for reliable communications

Addresses optimization problems in optical wavelength-routed networks

Describes several routing strategies for maximizing network utilization for various traffic-demand models

Considers routing problems in Internet Protocol (IP) networks

Presents mathematical puzzles that can be tackled by integer linear programming (ILP)

Using the GNU Linear Programming Kit (GLPK) package, which is designed for solving linear programming and mixed integer programming problems, it explains typical problems and provides solutions for communication networks. The book provides algorithms for these problems as well as helpful examples with demonstrations. Once you gain an understanding of how to solve LP problems for communication networks using the GLPK descriptions in this book, you will also be able to easily apply your knowledge to other solvers.

Reviews

"This textbook is intended to provide the fundamentals of linear programming as applied to communication networks and a practical guide on how to solve communication-related problems using linear programming solver. For this purpose, the GLPK package (a software package to solve linear programming problems, developed by Andrew O. Makhorin, freely available), which is intended for solving linear programming problems, integer linear programming problems and mixed integer linear programming problems, is adopted in this textbook. The book introduces and explains typical practical problems for communication networks and their solutions by providing sufficient programs of GLPK. The book also provides practical algorithms for these problems by solving helpful examples with demonstrations."

—Tiit Riismaa (Tallinn), Zentralblatt MATH 1322 | 1

Table of Contents

Optimization Problems for Communications Networks

Shortest path problem

Max flow problem

Minimum-cost flow problem

Basics of Linear Programming

Optimization problem

Linear programming problem

Simplex method

Dual problem

Integer linear programming problem

GLPK (GNU Linear Programming Kit)

How to obtain GLPKand install it

Usage of GLPK

Basic Problems for Communication Networks

Shortest path problem

Linear programming problem

Dijkstra’s algorithm

Bellman-Ford algorithm

Max flow problem

Linear programming problem

Ford-Fulkerson algorithm

Max flow and minimum cut

Minimum-cost flow problem

Linear programming problem

Cycle-canceling algorithm

Relationship among three problems

Disjoint Path Routing

Basic disjoint path problem

Integer linear programming problem

Disjoint shortest pair algorithm

Suurballe’s algorithm

Disjoint paths with shared risk link group

Shared risk link group (SRLG)

Integer linear programming

Weight-SRLG algorithm

Disjoint paths in multi-cost networks

Multi-cost networks

Integer linear programming problem

KPA: k-penalty with auxiliary link costs matrix

KPI: k-penalty with initial link costs matrix

Performance comparison of KPA and KPI

Optical Wavelength-Routed Network

Wavelength assignment problem

Graph coloring problem

Integer linear programming

Largest degree first

Routing and Traffic-Demand Model

Networkmodel

Pipemodel

Hosemodel

HSDT model

HLT model

IP Routing

Routing protocol

Link weights and routing

Tabu search

Preventive start-time optimization (PSO)

Three policies to determine link weights

PSOmodel

PSO-L

PSO-W

PSO-W algorithm based on tabu search

Performance of PSO-W

Mathematical Puzzles

Sudoku puzzle

Overview

Integer linear programming problem

River crossing puzzle

Overview

Integer linear programming approach

Shortest path approach

Comparison of two approaches

Lattice puzzle

Overview

Integer linear programming

A. Derivation of Eqs. (7.6a)–(7.6c) for hose model

B. Derivation of Eqs. (7.12a)–(7.12c) for HSDT model

C. Derivation of Eqs. (7.16a)–(7.16d) for HLT model

Answers to Exercises

Index

About the Author

Eiji Oki is an Associate Professor at the University of Electro-Communications, Tokyo, Japan. He received the B.E. and M.E. degrees in instrumentation engineering and a Ph.D. degree in electrical engineering from Keio University, Yokohama, Japan, in 1991, 1993, and 1999, respectively. In 1993, he joined Nippon Telegraph and Telephone Corporation (NTT) Communication Switching Laboratories, Tokyo, Japan. He has been researching network design and control, traffic-control methods, and high-speed switching systems. From 2000 to 2001, he was a Visiting Scholar at the Polytechnic Institute of New York University, Brooklyn, New York, where he was involved in designing terabit switch/router systems. He was engaged in researching and developing high-speed optical IP backbone networks with NTT Laboratories. He joined the University of Electro-Communications, Tokyo, Japan, in July 2008.

He has been active in THE standardization of path computation element (PCE) and GMPLS in IETF. He wrote more than ten IETF RFCs and drafts. He served as a Guest Co-Editor for the Special Issue on "Multi-Domain Optical Networks: Issues and Challenges," June 2008, in IEEE Communications Magazine; a Guest Co-Editor for the Special Issue on Routing, "Path Computation and Traffic Engineering in Future Internet," December 2007, in the Journal of Communications and Networks; a Guest Co-Editor for the Special Section on "Photonic Network Technologies in Terabit Network Era," April 2011, in IEICE Transactions on Communications; a Technical Program Committee (TPC) Co-Chair for the Workshop on High-Performance Switching and Routing in 2006, 2010 and 2012; a Track Co-Chair on Optical Networking for ICCCN 2009; a TPC Co-Chair for the International Conference on IP+Optical Network (iPOP 2010); and a Co-Chair of Optical Networks and Systems Symposium for IEEE International Conference on Communications (ICC 2011).

Prof. Oki was the recipient of the 1998 Switching System Research Award and the 1999 Excellent Paper Award presented by IEICE, the 2001 Asia-Pacific Outstanding Young Researcher Award presented by IEEE Communications Society for his contribution to broadband network, ATM, and optical IP technologies, and the 2010 Telecom System Technology Prize by the Telecommunications Advanced Foundation.

He has co-authored three books, Broadband Packet Switching Technologies, published by John Wiley, New York, in 2001, GMPLS Technologies, published by CRC Press, Boca Raton, FL, in 2005, and Advanced Internet Protocols, Services, and Applications, which will be published by Wiley in March 2012. He is an IEEE Senior Member.